Combining precoding with spectral shaping

ABSTRACT

In one embodiment, a device includes but is not limited to: a precoder having a precoder input and a precoder output; a spectral shaper, having a spectral-shaper transfer function and being operably coupled internal to said precoder; and a precoder filter, internal to the precoder, the precoder filter having a transfer function which provides substantially the inverse of the spectral-shaper transfer function.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present application relates, in general, to data communicationssystems.

2. Description of the Related Art

Data is information that is in a form suitable for manipulation and/orprocessing in a formalized manner, such as by one or more machines. Datacommunications systems are systems that transmit and/or receive datathrough at least one data communications link (e.g., a wireless link, awire link, or a fiber optic link).

Data communications systems often utilize what are known in the art as“modems.” “Modem” is short for modulator-demodulator. A modem is adevice or program that enables a computer to transmit data overtelephone lines or other communication media. Computer information isstored digitally, whereas information transmitted over telephone linesis transmitted in the form of analog waves. A modem converts betweenthese two forms.

The operations modems perform are complex, and there are many differentways in which such operations may be done. In the early days of datacommunications, different vendors devised their own unique ways of doingmodem operations. In order to communicate, both a transmitting and areceiving station had to use modems which understood the differentschemes of the various different vendors, or communications between thetwo was impossible.

Over time, the industry migrated to a standards based format. Under thestandards based format, various international bodies comprised ofindustry experts specified standards for interfaces and signals betweencommunicating modems, so that the communicating modems did not have toknow all the various unique ways in which the various vendors performedtheir modem operations. The idea underlying standards is that theinterfaces and signal exchanges are agreed to, but the various vendorsare free to provide such standard interfaces and signal exchangeshowever they see fit. One such standard is the V.90 modem standard ofthe International Telecommunication Union (ITU).

The V.90 standard is for 56-Kbps modems and was approved by theInternational Telecommunication Union (ITU) in February 1998. The V.90standard was implemented to resolve a battle between two then-competingvendor-created 56 Kbps technologies: X2 from 3COM and K56flex fromRockwell Semiconductor.

The V.90 is essentially a “hybrid” modem standard, in that it specifiesthat continuous signal standard analog transmission modem techniques(e.g., QPSK modulation) be used to transmit data, from a “client” modemto a “server” modem (e.g., in the “upstream” direction), over thephysical data transmission medium spanning the two modems, but thatdiscrete signal Pulse Amplitude Modulation (PAM) be used to transmitdata, from the server modem to the client modem (e.g., in the“downstream” direction), over the physical data transmission mediumspanning the two modems.

Relatively recently, an improvement upon the V.90 standard, known as theV.92 modem standard, has been approved. In the V.92 modem standard, ithas been proposed that discrete signal PAM be used to transmit data, inboth the upstream and the downstream directions, over the physical datatransmission medium spanning the two modems, typically over unshieldedtwisted pair lines (UTP).

V.92 is designed to minimize Pulse Code Modulation (PCM) codecquantization noise in both upstream and downstream directions. Itemploys non-equally spaced constellations to closely match PCM codecquantization levels (e.g. μ-law codec in North America and A-law code inEurope), on an attempt to minimize codec quantization noise. For modernPCM modem design, PCM codec quantization noise is considered one of thedominant impairments that affect modem performance (bit error rate).

There exist several well-known side effects of the use of non-equallyspaced constellations, such as increase of peak-to-average (power) ratio(PAR), reduced minimum distance for a given average power and so on.However, quantization noise reduction due to use of PCM (codec-matched)constellation levels significantly outweighs the above “side” effects.Therefore, both V.90 and V.92 modems yield much high data rates than theconventional modem technologies such as V.34 when transmitting over aPCM channel.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 shows a high-level block diagram of a precoding pulse amplitudemodulated (PAM) data communications system architecture 150.

FIG. 2 depicts a typical V.92 upstream channel response of a simulatedsystem

FIG. 3 illustrates, that, for a simulated system having noted simulationparameters, the power spectrum of a precoded signal x(n) has becomehighly colored.

FIG. 4 shows precoding architecture 450, which provides spectral shapingor additional spectral whitening.

FIG. 5 depicts a high-level block process flow chart showing atransmitter precoding scheme according to the subject matter of thepresent application.

FIG. 6 illustrates one possible approach to find the optimum i(n)according to a given cost function.

FIG. 7 shows a high-level logic flow chart of an implementation oftransmitter precoding spectral shaper S(D).

FIG. 8 depicts a high-level logic flow chart of an implementation ofupdating a spectral shaper to minimize |y(n)| (whitening).

FIG. 9 illustrates a high-level logic flow chart of an implementation ofupdating a spectral shaper to minimize RDS (DC notching).

The use of the same symbols in different drawings typically indicatessimilar or identical items.

DETAILED DESCRIPTION

Table of Contents of Detailed Description

-   A. Introduction-   B. PCM Based Precoding System Architecture of FIG. 1    -   1. Digital Data Bit Stream of FIG. 1    -   2. Bits-To-PAM Encoder of FIG. 1        -   a. Overview of Bits-to-PAM Encoder        -   b. Operation of Bits-to-PAM Encoder    -   3. Precoder of FIG. 1        -   a. Overview of Precoder        -   b. Operation of Precoder            -   i. Extended PAM Constellation Mapper of Precoder            -   ii. Precoder Filter of Precoder                -   i(n) Selection Block of Precoder    -   4. Prefilter of FIG. 1        -   a. Overview of Prefilter        -   b. Operation of Prefilter-   C. Inventor Has Discovered that Precoding Systems Using    Non-Equispaced PAM Undesirably Color the Transmit Power Spectrum    -   1. When V.92 Architecture Uses Non-Uniformly Spaced PAM, The        Transmit Power Spectrum Is Highly Colored-   D. Inventor Has Discovered that Precoding System Operation Can Be    Combined with Spectral Shaping    -   1.Modifying Precoding Architecture to Obtain Desired Spectrum    -   2.Inserting A Spectral Shaper Into a Precoding Acrchitecture        A. Introduction

As noted in the description of the related art, the V.92 standard hasbeen proposed as an improvement on the V.90 standard. As also noted inthe description of the related art, the inventor named herein hasdiscovered previously unrecognized problems with a straightforwardimplementation of the proposed V.92 standard. As will be disclosedbelow, the inventor has discovered solutions to these problems.

In devising the V.92 standard, the standard designers made changes tothe operation of the PAM system. As will be described in more detailbelow, the inventor named herein (“inventor”) has discovered that suchchanges yield unexpected transmit spectral coloring. If it is notproperly corrected, it does in fact adversely affect the operation ofthe PAM system; such discovery forms part of the inventive contentherein.

With respect to the PCM based precoding system architecture, it has beendiscovered by the inventor that, due to non-equally spacedconstellations used by extended PAM constellation mapper c[m] 104, theoutput spectrum of the transmitter precoder 130 will no longer be whiteand it is normally determined by the analog channel impulse response andconstellation used in transmission. For most analog channels ofinterest, it has been discovered by the inventor that transmit spectrumof a straightforward implementation of the V.92 transmitter as specifiedin V.92 standard will potentially produce one or multiple spectralspikes at frequencies where analog channel band-edges reside. Theseunwanted spectral spikes, if unsuppressed, will have damaging impactssuch as (1) disrupting local echo cancellation (EC) operation, (2)increasing transmit power, (3) increasing of PAR, (4) exciting ofinter-modulation products when passing through a nonlinear device (suchas transformer in a hybrid), (5) potentially violating of transmit powerspectral density (PSD) mask imposed by regional regulatory rules.

In other applications, where a desired goal is to place spectral nullsat particular frequencies, a common goal is to introduce a null in thespectrum at DC, thereby enabling transmission of a baseband PAM waveformover a channel that cannot accommodate a DC component in the datasignal. An alternative for such a channel would be to use passband PAM,but in many applications baseband PAM in conjunction with line codingand/or transmitter precoding is a most cost-effective alternative. SeeG. D. Forney, Jr. & A. R. Calderbank, propose to add spectral nullsusing transmitter precoding (see G. D. Forney, Jr. & A. R. Calderbank,Cost Codes for Partial Response Channels; or Cost Codes with SpectralNulls, IT-35 IEEE Trans. Information, 1989, at 925).

Spectral shaping is not as big an issue in passband systems as baseband,for several reasons. Baseband systems, particularly those operating overunshielded twisted pair cables (e.g. telephone lines) or digitalsubscriber lines (DSL), typically have a large variation in attenuationover the Nyquist bandwidth and also a large variation in cross-talkcoupling loss. Hence, there is much that can be done to improve theperformance of these systems by control of the transmitted powerspectrum. Passband systems, in contrast, usually have a relativeconstant attenuation vs. frequency because the bandwidth is narrowrelative to the center frequency, and cross-talk coupling may not be anissue or is relatively frequency independent.

The transmit spectrum can be controlled by introducing a controlledcorrelation among transmit symbols in the form of redundancy. A popularway to control the spectrum is through the design of a line code. See P.A. Franaszek, Sequence-state coding for digital transmission, 47 BSTJ,January 1968 at 143; and A. R. Calderband and J. E. Mazo, Spectral Nullsand Coding with Large Alphabets, IEEE Comm Mag., December 1991. In thepresent invention, the inventor proposes a way to control the spectrumthrough combining precoding and spectral shaping. One major motivationin baseband systems is the problem of baseline wander introduced by thealternating current (“AC”) coupling inherent in transformers andbroadband amplifiers. The effect of AC coupling in a channel is a formof Intersymbol Interference (ISI) called baseline wander ISI. Theundesired baseline wander ISI, a consequence of the zero at DC in thechannel response is a major consideration in spectral shaping.

Those having ordinary skill in the art will appreciate that the V.92standard, as well as the V.90 standard, represents a radical departurefrom previously-existing modem techniques. In particular, the V.92standard calls for direct transmission of PAM pulses onto the analogtransmission medium spanning a transmitting and a receiving station,rather than modulating an analog carrier as in previously-existing modemtechniques.

More importantly, both V.90 and V.92 use non-equally spacedconstellations in order to match PCM nonlinear analog-to-digitalconverter (ADC) or digital-to-analog converter (DAC) quantization levels(mu-law and A-law codec), as well as any digital impairments (Pad androbbed-bit signaling). For V.92 upstream (client to central office)transmission, the analog channel must be equalized before the signalreaches the PCM codec. This dictates that the entire analog channelequalization task in V.92 must be done in a transmitter by usingtransmit preceding and pre-filtering.

In order to provide a clear understanding of the problems detected bythe inventor, as well as the proposed solutions to such problems, thefollowing description is organized as follows. First, a PCM basedPrecoding System Architecture, representative of theforegoing-referenced straightforward implementation of V.92 standardprecoding system architecture, but with additional inventor insights, isdescribed. Second inventor discoveries regarding the fact that precodingsystems using non-equispaced PAM (e.g., V.92 Precoding Systems)undesirably color the transmit power spectrum are described. Third,various inventor solutions to the identified problems are described.

B. PCM Based Precoding System Architecture of FIG. 1

With reference to the figures, and with reference now to FIG. 1, shownis a high-level block diagram of a precoder pulse amplitude modulated(PAM) data communications system architecture 150, which isrepresentative of the foregoing-referenced straightforwardimplementation V.92 standard scheme, but with certain additionalinventor insights shown. Depicted is that digital data b(j) serves as aninput to bits-to-PAM encoder 100. The output of bits-to-PAM encoder 100serves as an input to precoder 130 (which is explained in detail below).Shown is that the output of precoder 130 serves as an input to prefilter110. The output of prefilter 110 feeds to into analog channel 112. Eachof the foregoing-referenced portions of the PAM data communicationsarchitecture 150 will be described in separately outlined sections,below.

Specifically, the digital data stream, bits-to-PAM encoder 100,precorder 130, and prefilter 110 will now be discussed in more detail.

1. Digital Data Bit Stream of FIG. 1

Illustrated is a data bit stream, {b(j)}, which represents a string ofbits (e.g., 101 110 001 . . . ), and which is typically generated by auser (not shown) of the system. The data bit stream, {b(j)}, feeds intobits-to-PAM encoder 100.

2. Bits-To-PAM Encoder of FIG. 1

a. Overview of Bits-to-PAM Encoder

Those having ordinary skill in the art will appreciate that, for anyphysical transmission medium spanning a transmitting station and areceiving station, there is a finite uppermost limit on how fast thesignal on the physical medium can be changed without the signalexperiencing severe distortion on its trip to the receiving station.Consequently, it is common in the art to “encode” a series of bits(e.g., three bits) into a “symbol,” and thereafter transmit that“symbol” over the communications medium. This encoding scheme allowsmore bits to be sent between the transmitting station and a receivingstation than would be possible should the bits have been sentindividually. One way in which the V.92 standard indicates thatforegoing may be done is to encode a series of bits into differentvoltage amplitudes (where each discrete voltage amplitude constitutes a“symbol”), such that each sequence of bits is uniquely paired with avoltage amplitude level. For example, each integer of the 8 (0–7)integers represented by a three-bit string could be uniquely paired witheach of 8 discrete voltage levels (e.g., 000 uniquely paired with afirst voltage level, 001 uniquely paired with a second voltage level,etc., all the way up to 111 uniquely paired with an eighth voltagelevel). The foregoing is essentially the function of bits-to-PAM encoder100.

b. Operation of Bits-to-PAM Encoder

Bits-to-PAM encoder 100 encodes a group of B bits into a PAM symbol,K(n) (actually, a discrete voltage level pulse), where n represents asymbol index (the use of this notation, where n represents a symbolindex, will prove particularly helpful following in that such notationallows tracking the progress of a single PAM symbol (or discrete voltagepulse) through the system. For a symbol-by-symbol based PAM encoder, M,the number of discrete PAM symbols, or voltage levels, is given by therelation M=2^(B). Illustrated is that Bits-to-PAM encoder 100 outputsits symbols, K(n), to summing junction 102 of precoder 130. As an aside,the inventor points out that, for a frame-based PAM encoder, the encoderwill take a frame (or multiple frames) of data bits and map them intomultiple PAM symbols by means of multiple modulus conversion (asspecified in V.90/V.92 standards) or shell mapping (as in V.34 spec);furthermore, the PAM encoder can also be used in conjunction withtrellis-coded modulation (TCM) (as in V.92 and V.34). The invention istherefore useful with many other systems besides the V.90 and V.92,those being used only as one example of how the invention isincorporated into a communication system.

3. Precoder of FIG. 1

a. Overview of Precoder

Those having ordinary skill in the art will appreciate that transmitterpreceding is complex, but known in the art. However, as an aid tounderstanding, the inventor provides the following overview. For moredetailed background information, the inventor directs the reader to thefollowing references: M. Tomlinson, New-automatic Equalizer EmployingModulo Arithmetic, 7 Electron Letter, March, 1971, at 138–139; H.Harashima & H. Miyakawa, Matched-transmission Techniques for Channelswith Intersymbol Interference, COM-20 IEEE Trans. On Communications,August, 1972, at 774; and G. D. Forney, Jr. & M. V. Eyuboglu, CombinedEqualization and Coding Using Precoding, 30 IEEE Comm. Magazine No. 12,December 1991, at 25–35.

By way of overview, those skilled in the art will recognize that adecision-feedback equalizer (DFE) is a nonlinear receiver structure thatoffers a good compromise between performance and implementationcomplexity (for more background information, please see J. G. Proakis,Digital Communications, 4^(th) Edition, McGraw-Hill Book Co., New York,2001). One potential problem with the DFE is that any decision errors atthe output of the decision device (slicer) will cause a corruptedestimate of the postcursor Inter-Symbol Interference (ISI) to begenerated by the postcursor equalizer. This phenomenon is called errorpropagation.

Those skilled in the art will appreciate that DFE error propagation canbe avoided by using transmitter precoding. There are several differentvariations of precoders (e.g., Forney, G. D., Jr. & Ungerboeck, G.,Modulation and coding for linear Gaussian channels, 44 IEEE Transactionson Information Theory, October 1998 at 2384–2415), one of which issometimes called a Tomlinson-Harashima precoder (THP), in honor of itsco-inventors. See M. Tomlinson, New-automatic Equalizer Employing ModuloArithmetic, 7 Electron Letter, March, 1971, at 138–139; see also H.Harashima & H. Miyakawa, Matched-transmission Techniques for Channelswith Intersymbol Interference, COM-20 IEEE Trans. On Communications,August 1972, at 774.)

Those skilled in the art will appreciate that the idea of preceding isto move the cancellation of the postcursor ISI to the transmitter sincethe data symbols are available at the transmitter. Assume there is afeed-forward filter that produces a causal impulse response (onlypostcursor ISI) and this impulse response is known to the transmitter.In practice, this impulse response must be estimated in the receiverusing adaptive filter techniques (e.g., such as those described inProakis' Digital Communications), and passed back to the transmitter inorder to use transmitter precoding. Those skilled in the art willappreciate that this is feasible on channels that are time-invariant orslowly time-varying.

A linear filter placed at the transmitter to invert the channel would beunstable if the channel has zeros in its transfer function, which wheninverted, leads to unstable poles. A Tomlinson and Harashima precoderuses a nonlinear filter that can invert a causal impulse response, butwhich does not have the potential for error propagation or for unstableoperation. The arrangement is shown in FIG. 1 where an equivalentchannel with D-transfer function P(D) is equalized (precoded) at thetransmitter.

A THP has the advantage that error propagation is eliminated and thenoise at the receiver is not colored. Another virtue of placing a DFEcapability at the transmitter is to eliminate the difficultiesassociated with combining the decoding the Trellis-coded modulation(TCM) which provides delayed decisions and conventional DFE whichrequires immediate decisions. See G. D. Forney, Jr. and M. V. Eyuboglu,“Combined Equalization and Coding Using Precoding,” IEEE Comm. Magazine,Vol. 30, No. 12, pp. 25–35, December 1991.

Another advantage of the THP has to do with the statistics of theprecoded symbols x(n). Under the continuous approximation and theassumption that the symbol alphabet M, is large, the x(n) areindependent and uniformly distributed random variables. This impliesthat the statistics of the precoded symbols are very similar to thestatistics of the original data symbols. This in turn implies that thespectrum of the x(n) is white. The inventor will show below that when Mis finite and especially when the constellation levels are not uniformlyspaced, the precoder output will be not be independent and therefore itsspectrum will no longer white.

b. Operation of Precoder

Continuing to refer to FIG. 1, Precoder 130 includes summing junction102, extended PAM constellation mapper c[m] 104, summing junction 106,precoder filter 108, and i(n) selection block 114. The operation ofprecoder 130 is somewhat complex, and the operations of its componentparts are described in more detail below. However, as an aid tounderstanding, the inventor will first set forth a high level heuristicdescription of how the component parts of precoder 130 functiontogether, prior to discussing such parts in detail.

As those skilled in the art will appreciate, insofar as precoder filter108 is intended to supply the inverse transfer function of a channelwith equivalent transfer function P(D), the magnitude of the output,w(n), of precoder filter 108 can be extremely large, dependent upon thecharacteristics of the transfer function of the channel, P(D), and thevalue of the precoded symbol x(n), and in some instances may be so largethat the system becomes unstable if a regular (non-extended) PAMconstellation mapper is used.

As can be seen from FIG. 1, the precoded symbol x(n) is the output ofsumming junction 106, and the inputs to summing junction 106 are u(n),the output of extended PAM constellation mapper 104 and the output w(n)of the precoder filter 108. In other words,x(n)=u(n)+w(n).

Continuing to refer to FIG. 1, and assuming that extended PAMconstellation mapper 104 utilizes a mapping function C[m(n)]=2m(n)+1 (asan example), it follows that the output, u(n) of extended PAMconstellation mapper 104 will beu(n)=2m(n)+1.

Continuing to refer to FIG. 1, it can be seen that the input, m(n), toextended PAM constellation mapper 104 is the output of summing junction102. The inputs to summing junction 102 are K(n), the output ofbits-to-PAM encoder 100 and the output i(n)M of multiplication junction116. In other words,m(n)=K(n)+i(n)M,and the output of the precoder, for c[m(n)]=2m(n)+1, is,

$\begin{matrix}{{x(n)} = {{w(n)} + {u(n)}}} \\{= {{w(n)} + {2{m(n)}} + 1}} \\{= {{w(n)} + {2{K(n)}} + {{i(n)}\left( {2M} \right)} + 1}}\end{matrix}$For example, if M=8 (8-PAM), w(n)=102.25 and K(n)=5, then i(n) isselected so that |x(n)| is minimized, which yields i(n)=−7 and theprecoder output becomes x(n)=102.25+2×5+1+(−7)×2×8=1.25. It isstraightforward to verify that with C[m]=2m+1 (uniformly spaced PAM,i.e., constellation levels . . . , ±7, ±5, ±3, ±1) the precoder outputis bounded, i.e., |x(n)|≦M.

Continuing to refer to FIG. 1, it can be seen that i(n) is the output ofi(n) selection block 114. The value of i(n) is selected under a certaindefined design criterion (normally minimizing symbol-by-symbol outputpower of the precoder, i.e., [x(n)]² or simply |x(n) |) and −N≦i(n)<Nwhere we assume there are N positive constellation levels and N negativelevels. In other words, the value of i(n) is selected such that under acertain defined modulo arithmetic scheme the output, of extended PAMconstellation mapper 104 will substantially be the smallest number,under the defined modulo scheme, that is representative of K(n). If theminimum symbol-by-symbol precoder output power is the ultimate goal,then selecting i(n) is equivalent to performing a modulo M operation on(w(n)+2K(n)+1) if C[m]=2m+1 is used (A modulo scheme is often explainedby reference to counting on a 12 hour rotary clock face (which isrepresentative of a modulo 12 scheme); for example, in module 12 thenumber 17 is represented by 5 (e.g., 17−12=5), the number 29 isrepresented by 5 (e.g., 29−2(12)=5), and the number 41 is represented by5 (e.g., 41−3(12)=5), where the resultant modulo numbers can all beobtained by counting to the number of a 12 hour rotary clock face.)Thus, if you choose your modulo scheme sufficient to provide for allyour likely symbol values, you can substantially eliminate yourlikelihood of making the system become unstable by keeping the magnitudeof the value of x(n) bounded, so that even if the output, w(n), ofprecoder filter 108 is large, x(n), which is the sum of u(n) and w(n),can be kept bounded by ±M.

Continuing to refer to FIG. 1 and when a non-equally spacedconstellation is used and/or a different design criterion is imposedother than minimizing the precoder output power, the i(n) selectingprocedure in general will not be a simple modulo M operation but theoriginal rule will still apply, i.e., selecting i(n) such that a certaindesign criterion is met or a cost function is minimized.

The foregoing constitutes a high level heuristic description of precoder130. For a more detailed discussion, the reader is referred to thereferences described above. Each of the component parts of precoder 130will now be discussed in more detail.

i. Extended PAM Constellation Mapper of Precoder

Shown is that summing junction 102 outputs its symbols, m(n), toextended PAM constellation mapper C[m] 104. Depicted is that extendedPAM constellation mapper C[m] 104 outputs its symbols, u(n), to summingjunction 106.

Insofar as that the operation of extended PAM constellation mapper C[m]104 has been discussed above in relation to the inventor-discoveredproblems with the V.92 PAM scheme, a detailed description of itsoperation is not set forth here.

ii. Precoder Filter of Precoder

The present detailed description assumes a level of skill in the artencompassing modems, modem standards, numerical methods, statistics,digital signal processing, and digital filtering. The inventor pointsout that while the input data bit stream, {b(j)}, is in fact a digitalstream, and the subsequent mappings by the PAM constellation mappers areto discrete voltage levels, the digital filters shown and describedherein, although digital, are not performing operations related to thedigital, or discrete, nature of the PAM data. That is, although the PAMsystems described herein produce discrete square pulses, the digitalfilters and spectrum shapers described herein are not filtering on thedigital content produced by the pulse amplitude modulators, but insteadare filtering and shaping on the frequency components making up thediscrete square pulses. In addition, the inventor also points out thatthe operation of digital filters cannot generally be understood orreasoned out by sketching the behavior of such filters in the timedomain, in that each digital filter is usually the result of at leastone inverse mathematical transform of desired frequency domaincharacteristics, plus some empirical engineering work. For backgroundinformation on digital filters and digital signal processing (DSP) ingeneral, please see C. Bore, An Introduction to the Principles andPractise of Digital Signal Processing (2002); C. Bore, An Introductionto the Principles and Practise of FIR Digital Filters (2002); and C.Bore, An Introduction to the Principles and Practise of IIR DigitalFilters (2002), all of which are available for purchase as eBooks athttp://www.bores.com.

Illustrated is that precoder filter 108 outputs each symbol, w(n), tosumming junction 106. Precoder filter 108 is typically used in atransmitting station to pre-compensate for analog channel (amplitude andphase) distortion that will be experienced by signals as they propagatefrom the transmitting station to the receiving station. Precoder filter108's functionality is similar to that of decision-feedback equalizationresiding at a receiving station but with two distinct advantages: (a)no-error propagation; and (b) it can be used with TCM. Those havingordinary skill in the art will appreciate that, typically, thecoefficients of precoder filter 108 are acquired in the receivingstation and transferred back to the transmitting station. In a strictlyzero-forcing approach, the precoder coefficients are chosen to satisfyP(D)=F(D)C(D) (in D-transform) where C(D) is the analog channel responseand F(D) is any combined filter response besides C(D). For properoperation, P(D): should be monic, i.e., the center tap should be one.Furthermore, for most channels of interest, P(D) is forced to be causaland monic, i.e., the first tap of P(D) is set to one.

iii. i(n) Selection Block of Precoder

Returning attention now again to summing junction 106, shown is thatsumming junction 106 outputs its resultant signal, x(n), which is fedback through i(n) selection block 114, which uses an algorithm to choosea number i(n) such that, when K(n) is summed with i(n)M, and such sumsubsequently run through extended PAM constellation mapper C[m] 104, theoutput u(n) will subsequently generate a sequence of the precoder outputx(n) that meet or is close to a predefined design criterion (or costfunction). If the minimum power criterion is used, u(n) will fold w(n)toward the smallest magnitude that is equivalent to x(n) under thepredefined modulo scheme in use. Specifically, in one embodiment, i(n)selection block 114 selects i(n) to minimize x(n). The chosen i(n) and Menter multiplication block 116, whose output is then input to summingjunction 102.

4. Prefilter of FIG. 1

a. Overview of Prefilter

Those having ordinary skill in the art will appreciate that prefilter110 is particularly useful when feed-forward equalization is notfeasible at a receiving station (e.g., such as in V.92 upstream). It isnot required in all embodiments and need not be present. Those skilledin the art will appreciate that, if a feed-forward equalizer (FFE) canbe placed at the receiver, one would preferably use a FFE in thereceiver instead of a pre-filter in the transmitting station.

b. Operation of Prefilter

Continuing to refer to FIG. 1, shown is an embodiment in which thesumming junction 106 outputs its resultant symbol, x(n), to prefilter110. Preferably, prefilter 110 has filter coefficients chosen to producefilter response, F(D), sufficient to adequately compensate for channelphase distortion when used in conjunction with precoder filter 108.

Prefilter 110 outputs its filtered symbol, z(n) to analog channel 112,which is a mathematical model of the physical characteristics ofinterest of the medium spanning the transmitting station and thereceiving station. Those having ordinary skill in the art willappreciate that, typically, the channel of interest is modeled as alinear channel with response C(D). Further depicted is the injection ofv(n), a mathematical model of additive noise.

C. Inventor has Discovered that Precoding Systems Using Non-EquispacedPAM Undesirably Color the Transmit Power Spectrum

As noted previously, in devising the V.92 standard, the standarddesigners made what superficially appeared to be minor changes to thepreviously-existing operation of the PAM system, but these changes havebeen found by the inventor to adversely affect system performance.

Again, the V.92 standard is just one example where the invention isuseful, and other communication systems may also make use of theinvention as will be apparent to a person skilled in the art, includingbut not limited to all communications systems that use precoding, suchas SHDSL (Symmetric High-Bitrate Digital Subscriber Loop) of the ITU991.2 specification.

Continuing to refer to FIG. 1, depicted is that precoder filter 108calculates filter output as

${w(n)} = {\sum\limits_{k = 1}^{L}{{x\left( {n - k} \right)}\mspace{11mu}{p(k)}}}$where we assume P(D) is a finite impulse response (FIR) filter (w/lengthof L) without loss of generality. The precoder output, x(n), is formedas:

${x(n)} = {{{u(n)} + {w(n)}} = {{u(n)} + {\sum\limits_{k = 1}^{L}{{x\left( {n - k} \right)}\mspace{11mu}{p(k)}}}}}$where u(n) is the output of the extended constellation mapper,u(n)=C[m(n)] and m(n) is given as m(n)=i(n)M+K(n) where K(n) is theoutput of the PAM encoder. The integer multiplier i(n) is selected suchthat |x(n)| or the instant (symbol-by-symbol) power of x(n) isminimized.

The inventor points out that a conventional (e.g. uniformly spaced) PAMsystem uses equispaced PAM. For example, a system that takes {±1, ±3, .. . } as its PAM voltage levels, and uses an extended PAM constellationmapping function of C[m]=2m+1 that can be accomplished by a simplemodulo M operation. In contrast, the inventor points out that the V.92PAM system (representative of systems using non-uniformly spaced PAM)specifies non-uniformly spaced PAM, and the extended PAM constellationmapper is either a listed table with a finite number of levels or anexplicit function of a mapping index, e.g. C[m]=ƒ(m) following A-law orμ-law rules.

1. When V.92 Architecture Uses Non-Uniformly Spaced PAM, the TransmitPower Spectrum is Highly Colored

As noted above, in devising the V.92 standard, the designers made whatsuperficially appeared to be minor changes to the previously-existingoperation of the PAM system. Namely, that the extended PAM constellationmapper C[m] 104 would use non-uniformly spaced PAM, the V.92 standardsystem. However, the inventor has unexpectedly discovered that if such achange is made, the V.92 standard system will not always functionsubstantially similarly to conventional (e.g. uniformly spaced) PAMsystems.

The inventor points out that the conventional PAM systems dictate thatextended PAM constellation mapper C[m] 104 use uniformly spaced PAM. Thereason for this is that for uniformly spaced PAM and C[m]=2m+1, theprecoding procedure will be constructed sufficient to ensure that|x(n)|≦M by selecting proper i(n). It has been found empirically that,with M large and a severely distorted channel, the distribution(statistical) of x(n) is almost uniformly distributed over [−M, M] andhence its frequency spectrum tends to be white.

The inventor points out that in the V.92 standard, the optimum extendedPAM constellation mapper C[m] 104 uses non-uniformly spaced PAMconstellation points that tend to match the underlying central office(CO) codec quantization grids. The inventor has determined that the useof non-uniformly spaced PAM results in degradation of communicationsystem performance.

As an illustrative example, the inventor essentially utilized the V.92communications system architecture, as described above, and considered anon-uniformly spaced PAM where C[m]=sign(m)+(1+m)|m| for all −N≦m<N withN being the maximum size of the extended constellation, and simulatedthe system on MATLAB, the results of which are shown in FIGS. 2 and 3and described herein.

Referring now to FIG. 2, depicted is a typical V.92 upstream channelresponse (e.g., as would appear if a PAM symbol, or square pulse,appeared at the output of precoder filter 108 of FIG. 1) of a simulatedsystem having the foregoing-noted simulation parameters. As can be seen,the magnitude of the upstream channel response is substantially flatacross the frequencies shown. As can also be seen, the frequencyresponse has a spike between zero and five hundred hertz.

With reference now to FIG. 3, illustrated is that, for the simulatedsystem having the foregoing-noted simulation parameters, the powerspectrum of the precoded signal x(n) has become highly colored. Theinventor has found that this undesirable coloring results when thenon-uniformly spaced constellation levels of the V.92 standard are used.In particular, the inventor has found that the 10 dB spectral spikearound 120 Hz can cause numerous problems at the receiving station. Theinventor notes that a smooth spectrum is usually desired for normalcommunications operation.

D. Inventor has Discovered that Precoding System Operation can beCombined with Spectral Shaping

As noted above, the inventor has discovered that the use ofnon-uniformly spaced PAM in V.92 systems results in undesirable coloringof the signal power spectrum of the precoded symbols, x(n). The inventorhas determined that it is advantageous to reduce such undesirablecoloring of x(n) due to the non-equally spaced constellation that isrequired in V.92.

As a related problem, it is desired in some applications that a certainspectral shape is required to ensure proper operation. For example, manybaseband systems use transformer coupling or AC-coupled electronics,which implies that the channel has infinite loss at DC Therefore, atransmit spectrum with DC notched is highly desirable for this channel.

Spectral nulls can be inserted at one frequency or finite set offrequencies using a filter in the transmitter. Transmit filtering oftenhas the undesired side effect of increasing peak transmitted power.Also, a fully equalized receiver will try to compensate signal loss atfrequencies where spectral nulls are introduced. Therefore, transmitterpreceding should be used in conjunction with spectral shaping, or linecoding can be used to achieve the same goal.

1. Modifying Precoding Architecture to Obtain Desired Spectrum

As noted above, the inventor has determined that it is highly desirablethat the transmit power spectrum of the individual symbols, x(n),emerging from the output of precoder 130, be approximately white underthe continuous approximation (M is large) and the assumption thatconstellation is evenly spaced. In one implementation, the inventionensures that the transmit power spectrum of the individual symbols,x(n), emerging from the output of precoder 130, be approximately whiteby treating the coloring as “unwanted signal components,” and adjustingthe architecture so that such “unwanted signal components” areminimized.

Specifically, as set forth above, the inventor has determined that theuse of non-uniformly spaced PAM constellation results in the transmitpower spectrum of the individual symbols, x(n), emerging from the outputof precoder 130, having one or more power spikes at various frequencies.The inventor is also aware that the “cost function” of the precodingarchitecture can be adjusted such that it tends to minimize what aredefined to be unwanted signal components as well as transmit power. Withreference again to the precoding architecture of FIG. 1, selecting i(n)is done such that a cost function defined as below is minimized,

${J(n)} = {{\alpha\mspace{11mu}{{x(n)}}^{2}} + {\left( {1 - \alpha} \right){{\sum\limits_{k = 0}^{n}{x(k)}}}^{2}}}$where 0≦α≦is a constant. If α=1, the cost function will reduce to thatof the conventional precoder. A similar but not completely identicalcost function can be used to achieve the same goal,

${J(n)} = {{\alpha\mspace{11mu}{{x(n)}}} + {\left( {1 - \alpha} \right){{{\sum\limits_{k = 0}^{n}{x(k)}}}.}}}$

As used herein, a term

${{RDS}(n)} = {\sum\limits_{k = 0}^{n}{x(k)}}$is called the running digital sum of the precoded signal x(n) and theRDS can be utilized to measure how much DC or low frequency componentsare in x(n). The RDS is a useful property of the DC notching because itpredicts accurately the magnitude of the baseline wander ISI for a lowcutoff frequency. When the RDS is bounded, there is a spectral null atDC. The above cost function ensures that the RDS is small and the outputpower of the precoder is also small. The design parameter 0≦α≦1 can beused to balance performance between DC notching (minimum DC power) andspectral whitening (minimum total power).

In a further embodiment of the subject matter of the presentapplication, the cost function can be combined with any other designrules. For example, this further embodiment allows to replace or to addcost functions to the above formula such as the running filter sum (RFS)described in a series of patents, including U.S. Pat. No. 5,970,100(issued Oct. 9, 1999), U.S. Pat. No. 6,192,087 (issued Feb, 20, 2001)and U.S. Pat. No. 6,278,744 (issued Aug. 21, 2001) all to SverrirOlafsson, Zhenyu Zhou and Xuming Zhang.

Specifically, the inventor has noted that insofar as the frequenciesassociated with the one or more transmit power spectrum spikes (orcolorings) are known, such spikes can be defined as “unwanted signalcomponents,” and the parameters of the precoder architecture adjustedaccordingly so that such unwanted spike components (or colorings) aresuppressed. The inventor points out that the cost function is functionof various parameters, and that the system designer can choose theparameters to optimize the cost (like adaptive filtering) utilizingoptimization procedures well known to those having ordinary skill in theart (e.g., adaptive solutions).

FIG. 5 depicts a high-level block process flow chart showing thetransmitter preceding scheme according to the subject matter of thepresent application. Method step 500 shows the start of the process.Method step 502 depicts the operation of the initialization of aprecoder (e.g., initialization of precoder 130). Method step 504illustrates the operation of receiving B bits (e.g. bits-to-PAM encoder100 receiving a series of bits).

Method step 506 shows the operation of mapping B bits to PAM symbol K(n)(e.g., bits-to-PAM encoder 100 outputting a symbol K(n) equivalent tothe received B bits referenced in method step 504). Method step 508depicts the operation of computing the output w(n) of the precoderfilter (e.g., the output of precoder filter 108).

Method step 510 illustrates the operation of engaging in the select i(n)procedure (e.g., as has herein described in relation to i(n) selectionblock 114). Method step 512 shows the operation of computingx(n)=w(n)+u(n) (e.g., as herein described in relation to the overalloperation of precoder 130).

Method step 514 depicts the operation of incrementing n, the symbolindex (e.g., as herein described in relation to the bits-to-PAM encoder100). Method step 516 illustrates an inquiry as to whether transmissionis complete. In the event that the inquiry of method step 516 yields adetermination that transmission is not complete, shown is that theprocess proceeds to method step 504 and continues as has been describedherein. In the event that the inquiry of method step 516 yields adetermination that transmission has been completed, shown is that theprocess proceeds to method step 518, which depicts the end of theprocess.

FIG. 6 shows one possible approach to find the optimum i(n) according toa given cost function. Method step 600 shows the start of the process.Method step 602 depicts the operation of setting J(n)=+inf. Method step604 illustrates the operation setting itmp=−N.

Method step 606 shows the operation of computingXtmp=w(n)+C[K(n)+itmp*M]. Method step 608 depicts the operation ofcomputing the cost function cost(n).

Method step 612 illustrates an inquiry as to whether cost(n)<J(n). Inthe event that the inquiry of method step 612 yields a determinationthat cost(n) is less than J(n), the process proceeds to method step 614,which depicts setting J(n)=cost(n), x(n)=Xtmp, and i(n)=itmp. In theevent that the inquiry of method step 612 yields a determination thatcost(n) is not less than J(n), the process proceeds to method step 616,which shows the operation of incrementing the symbol index n, andsetting itmp=itmp+1.

Method step 618 illustrates an inquiry as to whether itmp>N. In theevent that the inquiry of method step 618 yields a determination thatitmp is greater than N, the process proceeds to method step 620, whichdepicts obtaining the optimum x(n). In the event that the inquiry ofmethod step 618 yields a determination itmp is not greater than N, theprocess proceeds to method step 606, and continues in the fashiondescribed previously.

With respect to the above-mentioned cost function, when theabove-mentioned cost function is used, then the cost function iscalculated as follows: (1) compute the running digital sum using therecursive form RDS(n)=RDS(n−1)+x(n); (2) compute temporary cost functionas cost(n)=α|Xtmp|²+(1−α)|RSD(n−1)+Xtmp|². After the optimum i(n) isfound, the RDS is updated as RDS(n)=RDS(n−1)+x(n).

2. Inserting A Spectral Shaper Into a Precoding Architecture

As noted above, the inventor has determined that it is highly desirablethat the transmit power spectrum of the individual symbols, x(n),emerging from the output of precoder 130, be approximately white. In oneimplementation, the inventor ensures that the transmit power spectrum ofthe individual symbols, x(n), emerging from the output of precoder 130,be approximately white by treating the coloring as “unwanted signalcomponents,” and adjusting the precoder architecture so that such“unwanted signal components” are minimized.

One way in which the inventor has achieved the foregoing is to insert aspectral shaper S(D) into the precoder architecture. If the channel isideal, a Tomlinson precoder can be designed for the “channel” responseS(D) (actually a part of the transmitter). If the channel has anon-ideal response P(D), where P(D) is monic and causal, then theprecoder can be designed for the “channel” response P(D)S(D), which isalso monic and causal.

Referring now to FIG. 4, components provide spectral shaping oradditional spectral whitening. The architecture depicted in FIG. 4 issimilar to that shown and described in relation to FIG. 1, except thatin FIG. 4 the precoder system has been modified to include the presenceof a spectral shaper to ensure that the transmit power spectrum of thesymbol, y(n), emerging from spectral shaper system 400 will appearsubstantially “white,” while simultaneously ensuring that the presenceof the spectral shaper does not disrupt the operation of the othersystem components.

Specifically, shown in architecture 450 is a spectral shaper system 400having spectral response S(D). Precoder filter 108, having filterresponse P(D), of FIG. 1 has been modified to produce precoder filter408 which is such that the presence of the spectral shaper system 400 isessentially cancelled out from the resultant signal.

As can be seen in FIG. 4, this process will be transparent to the remotereceiver since the process does not change underlying channel response,in that the effects of the spectral response, S(D), in the directtransmit path and one in the precoder feedback path cancel out eachother as long as S(D) is invertible (i.e., no spectral nulls). Forconvenience, one may select

${{S(D)} = {1 + {\sum\limits_{i = 1}^{L_{s}}{s_{i}D^{i}}}}},$or use the vector s(n)=[s₁(n),s₂(n), . . . , s_(Ls)(n)] to represent thespectral shaper.

FIG. 7 shows a high-level logic flow chart of an implementation oftransmitter precoding spectral shaper S(D) according to the system ofFIG. 4. Method step 700 shows the start of the process. Method step 702shows the operation of the initialization of a precoder (e.g.,initialization of precoder 130). Method step 704 illustrates theoperation of receiving B bits (e.g. bits-to-PAM encoder 100 receiving aseries of bits).

Method step 706 shows the operation of mapping B bits to PAM symbol K(n)(e.g., bits-to-PAM encoder 100 outputting a symbol K(n) equivalent tothe received B bits referenced in method step 504). Method step 708depicts the operation of the updating a precoder filter using s(n−1) andp where s(n−1) represents the spectral shaper, and p represents thevector of the precoder coefficients. Method step 710 illustrates theoperation of computing precoder filter output w(n).

Method step 712 shows the operation of selecting i(n) to minimize|x(n)|. Method step 714 depicts the operation of computingx(n)=w(n)+u(n). Method step 716 illustrates the operation of updatings(n) to minimize the cost function. Method step 718 shows the operationof the incrementing n via the relationship of n=n+1. Method step 720depicts an inquiry as to whether transmission is complete. In the eventthat the inquiry of method step 720 yields a determination thattransmission is not complete, the process proceeds to method step 704and continues as has been described herein. In the event that theinquiry of method step 720 yields a determination that transmission hasbeen completed, the process proceeds to method step 722, which depictsthe end of the process.

After the spectral shaper s(n) is updated, the corresponding(L+L_(s)−1)-tap precoder coefficients can be recalculated as follows,q(n)=[p,0]+[s(n),0]+[0,p{circle around (×)}s(n)]where p=[p₁,p₂, . . . , p_(L)] is the vector of the original precodercoefficients, 0 represents any zero vectors for filling vectors p ands(n) up to the full length (L+L_(s)−1) and the operator {circle around(×)} represents vector convolution. Or equivalently,

${Q(D)} = {{1 + {\sum\limits_{i = 1}^{L + L_{s} - 1}{q_{i}D^{i}}}} = {{S(D)}{{P(D)}.}}}$

The inventor points out that a special case of the foregoing generalscheme may be understood as follows (as will be explained with respectto FIG. 8, described in detail following). The inventor points out that,in one implementation, the spectral response, S(D), can be selected oradaptively updated according to a variety of criteria. For spectralwhitening purposes, one may select S(D) such that |y(n)| is minimized.Then S(D) will be a forward linear predictor and can be adapted by usingthe LMS algorithm as follows:s _(i)(n)=s _(i)(n−1)−μy(n)x(n×i), i=1, 2, . . . ,L _(s)where μ is the step size.

FIG. 8 depicts a high-level logic flow chart of an implementation ofupdating a spectral shaper to minimize |y(n)| (whitening). Method step800 shows the start of the process of updating s(n) to minimize the costfunction. Method step 802 depicts an inquiry as to whether updating s(n)is desired. In the event that the inquiry of method step 802 yields adetermination that updating s(n) is not desired, shown is that theprocess proceeds to method step 808 and continues as described herein.In the event that the inquiry of method step 802 yields a determinationthat updating s(n) is necessary, shown is that the process proceeds tomethod step 804, which depicts computing y(n).

Method step 806 shows the operation of updatings(n)=s(n−1)−mu*x(n−1)*y(n). Method step 708 depicts the operation ofupdating a precoder filter using s(n−1) and p. Method step 808illustrates the operation of obtaining updated spectral shapercoefficient vector s(n).

For spectral shaping or DC/low frequency component removal, one canchoose S(D) to minimize the RDS of y(n). The LMS adaptation rule will bechanged to (e.g., see FIG. 9 described in detail following):s _(i)(n)=s _(i)(n−1)−μR _(y)(n)R _(x)(n−i), i=1, 2, . . . ,L _(s)where

${R_{y}(n)} = {{\sum\limits_{k = 0}^{n}{{y(k)}\mspace{14mu}{and}\mspace{14mu}{R_{x}(n)}}} = {\sum\limits_{k = 0}^{n}{x(k)}}}$are the running digital sums of y(n) and x(n), respectively.

FIG. 9 depicts a high-level logic flow chart of an implementation ofupdating a spectral shaper to minimize RDS (DC notching). Method step900 shows the start of the process of updating s(n) to minimize the costfunction. Method step 902 depicts an inquiry as to whether updating s(n)is desired. In the event that the inquiry of method step 902 yields adetermination that updating s(n) is not desired, shown is that theprocess proceeds to method step 912 and continues as described herein.In the event that the inquiry of method step 902 yields a determinationthat updating s(n) is desired, the process proceeds to method step 904,which depicts computing y(n).

Method step 906 shows the operation of computing RDS, Rx(n), from x(n).Method step 908 depicts the operation of computing RDS, Ry(n), fromy(n). Method step 910 illustrates the operation of updatings(n)=s(n−1)−mu*Rx(n−1)*Ry(n). Method step 912 shows the operation ofobtaining updated spectral shaper coefficient vector s(n).

Those having ordinary skill in the art will recognize that the state ofthe art has progressed to the point where there is little distinctionleft between hardware and software implementations of aspects ofsystems; the use of hardware or software is generally (but not always,in that in certain contexts the choice between hardware and software canbecome significant) a design choice representing cost vs. efficiencytradeoffs. Those having ordinary skill in the art will appreciate thatthere are various vehicles by which aspects of processes and/or systemsdescribed herein can be effected (e.g., hardware, software, and/orfirmware), and that the preferred vehicle will vary with the context inwhich the processes and/or systems are deployed. For example, if animplementer determines that speed and accuracy are paramount, theimplementer may opt for a hardware and/or firmware vehicle;alternatively, if flexibility is paramount, the implementer may opt fora solely software implementation; or, yet again alternatively, theimplementer may opt for some combination of hardware, software, and/orfirmware. Hence, there are several possible vehicles by which aspects ofthe processes described herein may be effected, none of which isinherently superior to the other in that any vehicle to be utilized is achoice dependent upon the context in which the vehicle will be deployedand the specific concerns (e.g., speed, flexibility, or predictability)of the implementer, any of which may vary.

The foregoing detailed description has set forth various embodiments ofthe devices and/or processes via the use of block diagrams, flowcharts,and examples. Insofar as such block diagrams, flowcharts, and examplescontain one or more functions and/or operations, it will be understoodas notorious by those within the art that each function and/or operationwithin such block diagrams, flowcharts, or examples can be implemented,individually and/or collectively, by a wide range of hardware, software,firmware, or virtually any combination thereof. In one embodiment, thepresent invention may be implemented via Application Specific IntegratedCircuits (ASICs). However, those skilled in the art will recognize thatthe embodiments disclosed herein, in whole or in part, can beequivalently implemented in standard Integrated Circuits, as one or morecomputer programs running on one or more computers (e.g., as one or moreprograms running on one or more computer systems), as one or moreprograms running on one or more controllers (e.g., microcontrollers) asone or more programs running on one or more processors (e.g.,microprocessors), as firmware, or as virtually any combination thereof,and that designing the circuitry and/or writing the code for thesoftware and or firmware would be well within the skill of one ofordinary skill in the art in light of this disclosure. In addition,those skilled in the art will appreciate that the mechanisms of thepresent invention are capable of being distributed as a program productin a variety of forms, and that an illustrative embodiment of thepresent invention applies equally regardless of the particular type ofsignal bearing media used to actually carry out the distribution.Examples of signal bearing media include, but are not limited to, thefollowing: recordable type media such as floppy disks, hard disk drives,CD ROMs, digital tape, and computer memory; and transmission type mediasuch as digital and analogue communication links using TDM or IP basedcommunication links (e.g., packet links).

In a general sense, those skilled in the art will recognize that thevarious embodiments described herein which can be implemented,individually and/or collectively, by a wide range of hardware, software,firmware, or any combination thereof can be viewed as being composed ofvarious types of “electrical circuitry.” Consequently, as used herein“electrical circuitry” includes, but is not limited to, electricalcircuitry having at least one discrete electrical circuit, electricalcircuitry having at least one integrated circuit, electrical circuitryhaving at least one application specific integrated circuit, electricalcircuitry forming a general purpose computing device configured by acomputer program (e.g., a general purpose computer configured by acomputer program which at least partially carries out processes and/ordevices described herein, or a microprocessor configured by a computerprogram which at least partially carries out processes and/or devicesdescribed herein), electrical circuitry forming a memory device (e.g.,forms of random access memory), and electrical circuitry forming acommunications device (e.g., a modem, communications switch, oroptical-electrical equipment).

The foregoing described embodiments depict different componentscontained within, or connected with, different other components. It isto be understood that such depicted architectures are merely exemplary,and that in fact many other architectures can be implemented whichachieve the same functionality. In a conceptual sense, any arrangementof components to achieve the same functionality is effectively“associated” such that the desired functionality is achieved. Hence, anytwo components herein combined to achieve a particular functionality canbe seen as “associated with” each other such that the desiredfunctionality is achieved, irrespective of architectures or intermedialcomponents. Likewise, any two components so associated can also beviewed as being “operably connected”, or “operably coupled”, to eachother to achieve the desired functionality.

From the foregoing it will be appreciated that, although specificembodiments of the invention have been described herein for purposes ofillustration, various modifications may be made without deviating fromthe spirit and scope of the invention. Specifically, those havingordinary skill in the art will appreciate that while the presentapplication describes difficulties relating to systems utilizingtransmitter precoding in conjunction with non-equally spacedconstellations, the teachings of the present application are not limitedto such systems, but are instead applicable to all communicationssystems analogous to those described in the application. Accordingly,the invention is not limited except as by the appended claims.

1. A pulse amplitude modulation (PAM) data communication systemcomprising: a bits to PAM encoder configured to receive a group of bitsand operable to encode the group of bits into discrete voltage levelpulses; a precoder coupled to the PAM encoder and configured to receivethe discrete voltage pulses and operable to generate precoded symbols,the precoder containing a precoder filter operable on the discretevoltage pulses to compensate for amplitude and phase distortion causedby propagation of a transmitted signal via a communication channel; aspectral shaper contained in the precoder and operable to providespectral whitening of the precoded symbols by minimizing unwanted signalcomponents; and a pre-filter coupled to the precoder and configured toreceive the precoded symbols, the pre-filter having filter coefficientsto compensate for channel phase distortion when used in conjunction withthe precoder filter, wherein the precoded symbols are transmitted overthe communication channel.
 2. The PAM data communication system of claim1, wherein the system is a modem.
 3. The PAM data communication systemof claim 1, wherein an input of the precoder filter is operably coupled,through a summing junction, to an output of an extended PAMconstellation mapper.
 4. The PAM data communication system of claim 1,wherein an output of the precoder filter is operably coupled, through asumming junction, to the spectral shaper.
 5. The PAM data communicationsystem of claim 1, wherein an output of the precoder filter is operablycoupled, through a summing junction, to a selection block.
 6. The PAMdata communication system of claim 5, wherein the selection blockperforms selection to substantially minimize the power of the output ofthe precoder filter under a modulo scheme.
 7. The PAM data communicationsystem of claim 6, wherein an output of the selection block is operablycoupled, through a summing junction, to an input of an extended PAMconstellation mapper.